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Aristotle's logic

Under Logic, Aristotle treats of the methods of arriving at general propositions, and of reasoning from them. His logic is at once the art of thinking and the instrument of thought. The completeness of our knowledge depends on the extent and completeness of our experience. His manner of reasoning is by the syllogism, an argument consisting of three propositions, such that the concluding one follows of necessity from the two premises, and of which, indeed, the whole theory of demonstration is only an example. Regarding logic as the instrument of thought, he introduces into it, as a fundamental feature, the ten categories. These predicaments are the genera to which everything may be reduced, and denote the most general of the attributes which may be assigned to a thing.

and metaphysics.

His metaphysics overrides all the branches of the physical sciences. It undertakes an examination of the postulates on which each one of them is founded, determining their truth or fallacy. Considering that all science must find a support for its fundamental conditions in an extensive induction from facts, he puts at the foundation of his system the consideration of the individual; in relation to the world of sense, he regards four causes as necessary for the production of a fact—the material cause, the substantial cause, the efficient cause, the final cause.

Temporary failure of his system.

But as soon as we come to the Physics of Aristotle we see at once his weakness. The knowledge of his age does not furnish him facts enough whereon to build, and the consequence is that he is forced into speculation. It will be sufficient for our purpose to allude to a few of his statements, either in this or in his metaphysical branch, to show how great is his uncertainty and confusion. Thus he asserts that matter contains a triple form—simple substance, higher substance, which is eternal, and absolute substance, or God himself; that the universe is immutable and eternal, and, though in relation The Peripatetic philosophy.

Substance, Motion, Space, Time. with the vicissitudes of the world, it is unaffected thereby; that the primitive force which gives rise to all the motions and changes we see is Nature; it also gives rise to Rest; that the world is a living being, having a soul; that, since every thing is for some particular end, the soul of man is the end of his body; that Motion is the condition of all nature; that the world has a definite boundary and a limited magnitude; that Space is the immovable vessel in which whatever is may be moved; that Space, as a whole, is without motion, though its parts may move; that it is not to be conceived of as without contents; that it is impossible for a vacuum to exist, and hence there is not beyond and surrounding the world a void which contains the world; that there could be no such thing as Time unless there is a soul, for time being the number of motion, number is impossible except there be one who numbers; that, perpetual motion in a finite right line The world. being impossible, but in a curvilinear path possible, the world, which is limited and ever in motion, must be of a spherical form; that the earth is its central part, the heavens the circumferential: hence the heaven is nearest to the prime cause of motion; that the orderly, continuous, and unceasing movement of the celestial bodies implies an unmoved mover, for the unchangeable alone can give birth to uniform motion; that unmoved existence is God; that the stars are passionless beings, having attained the end of existence, and worthy above other things of human adoration; that the fixed stars are in the outermost heaven, and the sun, moon, and planets beneath: the former receive their motion from the prime moving cause, but the planets are disturbed by the stars; that there are five elements—earth, air, fire, water, and ether; that the earth is in the centre of the world, since earthy matter settles uniformly round a central point; that fire seeks the circumferential region, and intermediately water floats upon the earth, and air upon water; that the elements are transmutable into one another, and hence many intervening substances arise; that each sphere is in interconnection with the others; the earth is agitated and disturbed by the sea, the sea by the winds, which are movements of the air, the air by the sun, moon, and planets. Each inferior sphere is controlled by its outlying or superior one, and hence it follows that the earth, which is thus disturbed by the conspiring or conflicting action of all above it, is liable to the most irregularities; that, since animals are nourished by the earth, it needs must enter into their composition, but that water is required to hold the earthy matters together; that every element must be looked upon as living, since it is pervaded by the soul of the world; that there is an unbroken chain from the simple element through the plant and animal up to man, Organic beings. the different groups merging by insensible shades into one another: thus zoophytes partake partly of the vegetable and partly of the animal, and serve as an intermedium between them; that plants are inferior to animals in this, that they do not possess a single principle of life or soul, but many subordinate ones, as is shown by the circumstance that, when they are cut to pieces, each piece is capable of perfect or independent growth or life. Their inferiority is likewise betrayed by their belonging especially to the earth to which they are rooted, each root being a true mouth; and this again displays their lowly position, for the place of the mouth is ever an indication of the grade of a creature: thus in man, who is at the head of the scale, it is in the upper part of the body; that in proportion to the heat of an animal is its grade higher; thus those that are aquatic are cold, and therefore of very little intelligence, and the same maybe said of plants; but of man, whose warmth is very great, the soul is much more excellent; that the possession of locomotion by an organism always implies the possession of sensation; that the senses of taste and touch indicate the qualities of things in contact with the organs of the animal, but that those of Physiological conclusions. smell, hearing, and sight extend the sphere of its existence, and indicate to it what is at a distance: that the place of reception of the various sensations is the soul, from which issue forth the motions; that the blood, as the general element of nutrition, is essential to the support of the body, though insensible itself: it is also essential to the activity of the soul; that the brain is not the recipient of sensations: that function belongs to the heart; all the animal activities are united in the last; it contains the principle of life, being the principle of motion: it is the first part to be formed and the last to die; that the brain is a mere appendix to the heart, since it is formed after the heart, is the coldest of the organs and is devoid of blood; that the soul is the reunion of all the functions of the body: it is an energy or active essence; being neither body nor magnitude, it cannot have extension, for thought has no parts, nor can it be said to move in space; it is as a sailor, who is motionless in a ship which is moving; that, in the origin of the organism, the male furnishes the soul and the female the body; that the body being liable to decay, and of a transitory nature, it is necessary for its well-being that its disintegration and nutrition should balance one another; that sensation may be compared to the impression of a seal on wax, the wax receiving form only, but no substance or matter; that imagination arises from impressions thus made, which endure for a length of time, and that this is the origin of memory; that man alone possesses recollection, but animals share with him memory—memory being unintentional or spontaneous, but recollection implying voluntary exertion or a search; that recollection is necessary for acting with design. It is doubtful whether Aristotle believed in the immortality of the soul, no decisive passage to that effect occurring in such of his works as are extant.

Causes of Aristotle's success and failure.

Aristotle, with a correct and scientific method, tried to build up a vast system when he was not in possession of the necessary data. Though a very learned man, he had not sufficient knowledge; indeed, there was not sufficient knowledge at that time in the world. For many of the assertions I have quoted in the preceding paragraph there was no kind of proof; many of them also, such as the settling of the heavy and the rise of the light, imply very poor cosmic ideas. It is not until he deals with those branches, such as comparative anatomy and natural history, of which he had a personal and practical knowledge, that he begins to write well. Of his physiological conclusions, some are singularly felicitous; his views of the connected chain of organic forms, from the lowest to the highest, are very grand. His metaphysical and physical speculations—for in reality they are nothing but speculations—are of no kind of value. His successful achievements, and also his failures, conspicuously prove the excellence of his system. He expounded the true principles of science, but failed to apply them merely for want of materials. His ambition could not brook restraint. He would rather attempt to construct the universe without the necessary means than not construct it at all.

Aristotle failed when he abandoned his own principles, and the magnitude of his failure proves how just his principles were; he succeeded when he adhered to them. If anything were wanting to vindicate their correctness and illustrate them, it is supplied by the glorious achievements of the Alexandrian school, which acted in physical science as Aristotle had acted in natural history, laying a basis solidly in observation and experiment, and accomplishing a like durable and brilliant result.

Biography of Zeno.

From Aristotle it is necessary to turn to Zeno, for the Peripatetics and Stoics stand in parallel lines. The social conditions existing in Greece at the time of Epicurus may in some degree palliate his sentiments, but virtue and honour will make themselves felt at last. Stoicism soon appeared as the antagonist of Epicureanism, and Epicurus found in Zeno of Citium a rival. The passage from Epicurus to Zeno is the passage from sensual gratification to self-control.

The biography of Zeno may be dismissed in a few words. Born about B.C. 300, he spent the early part of his life in the vocation of his father, who was a merchant, but, by a fortunate shipwreck, happily losing his goods during a voyage he was making to Athens, he turned to philosophy for consolation. Though he had heretofore been somewhat acquainted with the doctrines of Socrates, he became a disciple of the Cynics, subsequently studying in the Megaric school, and then making himself acquainted with Platonism. After twenty years of preparation, he opened a school in the stoa or porch in Athens, from which his doctrine and disciples have received their name. He presided over his school for fifty-eight years, numbering many eminent men among his disciples. When nearly a hundred years old he chanced to fall and break his finger, and, receiving this as an admonition that his time was accomplished, he forthwith strangled himself. The Athenians erected to his memory a statue of brass. His doctrines long survived him, and, in times when there was no other consolation for man, offered a support in their hour of trial, and an unwavering guide in the vicissitudes of life, not only to many illustrious Greeks, but also to some of the great philosophers, statesmen, generals, and emperors of Rome.

Intention of Stoicism.

It was the intention of Zeno to substitute for the visionary speculations of Platonism a system directed to the daily practices of life, and hence dealing chiefly with morals. To make men virtuous was his aim. But this is essentially connected with knowledge, for Zeno was persuaded that if we only know what is good we shall be certain to practise it. He therefore rejected Plato's fancies of Ideas and Reminiscences, leaning to the common-sense doctrines of Aristotle, to whom he approached in many details. With him Sense furnishes the data of knowledge, and Reason combines them: the soul being modified by external things, and modifying them in return, he believed that the mind is at first, as it were, a blank tablet, on which sensation writes marks, and that the distinctness of sensuous impressions is the criterion of their truth. The changes thus produced in the soul constitute ideas; but, with a prophetic inspiration, he complained that man will never know the true essence of things.

The Physics of Zeno.

In his Physics Zeno adopted the doctrine of Strato, that the world is a living being. He believed that nothing incorporeal can produce an effect, and hence that the soul is corporeal. Matter and its properties he considered to be absolutely inseparable, a property being actually a body. In the world there are two things, matter and God, who is the Reason of the world. Essentially, however, God and matter are the same thing, which assumes the aspect of matter from the passive point of view, and God from the active; he is, moreover, the prime moving force, Destiny, Necessity, a life-giving Soul, evolving things as the vital force evolves a plant out of a seed; the visible world is thus to be regarded as the material manifestation of God. The transitory objects which it on all sides presents will be reabsorbed after a season of time, and reunited in him. The Stoics pretended to indicate, even in a more definite manner, the process by which the world has arisen, and also its future destiny; for, regarding the Supreme as a vital heat, they supposed that a portion of that fire, declining in energy, became transmuted into matter, and hence the origin of the world; but that that fire, hereafter resuming its activity, would cause a universal conflagration, the end of things. During the present state everything is in a condition of uncertain mutation, decays being followed by reproductions, and reproductions by decays; and, as a cataract shows from year to year an invariable form, though the water composing it is perpetually changing, so the objects around us are nothing more than a flux of matter offering a permanent form. Thus the visible world is only a moment in the life of God, and after it has vanished away like a scroll that is burned, a new period shall be ushered in, and a new heaven and a new earth, exactly like the ancient ones, shall arise. Since nothing can exist without its contrary, no injustice unless there was justice, no cowardice unless there was courage, no lie unless there was truth, no shadow unless there was light, so the existence of good necessitates that of evil. The Stoics believed that the development of the world is under the dominion of paramount law, supreme law, Destiny, to which God himself is subject, and that hence he can only develop the world in a predestined way, as the vital warmth evolves a seed into the predestined form of a plant.

Exoteric philosophy of the Stoics.

The Stoics held it indecorous to offend needlessly the religious ideas of the times, and, indeed, they admitted that there might be created gods like those of Plato; but they disapproved of the adoration of images and the use of temples, making amends for their offences in these particulars by offering a semi-philosophical interpretation of the legends, and demonstrating that the existence, and even phenomenal display of the gods was in accordance with their principles. Perhaps to this exoteric philosophy we must ascribe the manner in which they expressed themselves as to final causes—expressions sometimes of amusing quaintness—thus, that the peacock was formed for the sake of his tail, and that a soul was given to the hog instead of salt, to prevent his body from rotting; that the final cause of plants is to be food for brutes, of brutes to be food for men, though they discreetly checked their irony in its ascending career, and abstained from saying that men are food for the gods, and the gods for all.

Their opinions of the nature of the soul.

The Stoics concluded that the soul is mere warm breath, and that it and the body mutually interpervade one another. They thought that it might subsist after death until the general conflagration, particularly if its energy were great, as in the strong spirits of the virtuous and wise. Its unity of action implies that it has a principle of identity, the I, of which the physiological seat is the heart. Every appetite, lust, or desire is an imperfect knowledge. Our nature and properties are forced upon us by Fate, but it is our duty to despise all our propensities and passions, and to live so that we may be free, intelligent, and virtuous.

Their ethical rules of wisdom.

This sentiment leads us to the great maxim of Stoical Ethics, "Live according to Reason;" or, since the world is composed of matter and God, who is the Reason of the world, "Live in harmony with Nature." As Reason is supreme in Nature, it ought to be so in man. Our existence should be intellectual, and all bodily pains and pleasures should be despised. A harmony between the human will and universal Reason constitutes virtue. The free-will of the sage should guide his actions in the same irresistible manner in which universal Reason controls nature. Hence the necessity of a cultivation of physics, without which we cannot distinguish good from evil. The sage is directed to remember that Nature, in her operations, aims at the universal, and never spares individuals, but uses them as means for accomplishing her ends. It is for him, therefore, to submit to his destiny, endeavouring continually to establish the supremacy of Reason, and cultivating, as the things necessary to virtue, knowledge, temperance, fortitude, justice. He is at liberty to put patriotism at the value it is worth when he remembers that he is a citizen of the world; he must train himself to receive in tranquillity the shocks of Destiny, and to be above all passion and all pain. He must never relent and never forgive. He must remember that there are only two classes of men, the wise and the fools, as "sticks can only either be straight or crooked, and very few sticks in this world are absolutely straight."

Rise of Greek science.

Political position of the Ptolemies.

From the account I have given of Aristotle's philosophy, it may be seen that he occupied a middle ground between the speculation of the old philosophy and the strict science of the Alexandrian school. He is the true connecting link, in the history of European intellectual progress, between philosophy and science. Under his teaching, and the material tendencies of the Macedonian campaigns, there arose a class of men in Egypt who gave to the practical a development it had never before attained; for that country, upon the breaking up of Alexander's dominion, B.C. 323, falling into the possession of Ptolemy, that general found himself at once the depositary of spiritual and temporal power. Of the former, it is to be remembered that, though the conquest by Cambyses had given it a severe shock, it still not only survived, but displayed no inconsiderable tokens of strength. Indeed, it is well known that the surrender of Egypt to Alexander was greatly accelerated by hatred to the Persians, the Egyptians welcoming the Macedonians as their deliverers. In this movement we perceive at once the authority of the old priesthood. It is hard to tear up by the roots an ancient religion, the ramifications of which have solidly insinuated themselves among a populace. That of Egypt had already been the growth of more than three thousand years. The question for the intrusive Greek sovereigns to solve was how to co-ordinate this hoary system with the philosophical scepticism They co-ordinate Egyptian idolatry and Greek scepticism. that had issued as the result of Greek thought. With singular sagacity, they saw that this might be accomplished by availing themselves of Orientalism, the common point of contact of the two systems; and that, by its formal introduction and development, it would be possible not only to enable the philosophical king, to whom all the pagan gods were alike equally fictitious and equally useful, to manifest respect even to the ultra-heathenish practices of the Egyptian populace, but, what was of far more moment, to establish an apparent concord between the old sacerdotal Egyptian party—strong in its unparalleled antiquity; strong in its reminiscences; strong in its recent persecutions; strong in its Pharaonic relics, regarded by all men with a superstitious or reverent awe—and the free-thinking and versatile Greeks. The occasion was like some others in history, some even in our own times; a small but energetic body of invaders was holding in subjection an ancient and populous country.

The Museum of Alexandria.

To give practical force to this project, a grand state institution was founded at Alexandria. It became celebrated as the Museum. To it, as to a centre, philosophers from all parts of the world converged. It is said that at one time not less than fourteen thousand students were assembled there. Alexandria, in confirmation of the prophetic foresight of the great soldier who founded it, quickly became an immense metropolis, abounding in mercantile and manufacturing activity. As is ever the case with such cities, its higher classes were prodigal and dissipated, its lower only to be held in restraint by armed force. Its public amusements were such as might be expected—theatrical shows, music, horse-racing. In the solitude of such a crowd, or in the noise of such dissipation, anyone could find a retreat—atheists who had been banished from Athens, devotees from the Ganges, monotheistic Jews, blasphemers from Asia Minor. Indeed, it has been said that in this heterogeneous community blasphemy was hardly looked upon as a crime; at the worst, it was no more than an unfortunate, and, it might be, an innocent mistake. But, since uneducated men need some solid support on which their thoughts may rest, mere abstract doctrines not meeting their wants, it became necessary to provide a corporeal representation Establishment of the worship of Serapis. for this eclectic philosophical Pantheism, and hence the Ptolemies were obliged to restore, or, as some say, to import the worship of the god Serapis. Those who affirm that he was imported say that he was brought from Sinope; modern Egyptian scholars, however, give a different account. As setting forth the Pantheistic doctrine of which he was the emblem, his image, subsequently to attain world-wide fame, was made of all kinds of metals and stones. "All is God." But still the people, with that instinct which other nations and ages have displayed, hankered after a female divinity, and this led to the partial restoration of the worship of Isis. It is interesting to remark how the humble classes never shake off the reminiscences of early life, leaning rather to the maternal than to the paternal attachment. Perhaps it is for that reason that they expect a more favourable attention to their supplications from a female divinity than a god. Accordingly, the devotees of Isis soon out-numbered those of Serapis, though a magnificent temple had been built for him at Rhacotis, in the quarter adjoining the Museum, and his worship was celebrated with more than imperial splendour. In subsequent ages the worship of Serapis diffused itself throughout the Roman empire, though the authorities—consuls, senate, emperors—knowing well the idea it foreshadowed, and the doctrine it was meant to imply, used their utmost power to put it down.

The Alexandrian libraries.

The Alexandrian Museum soon assumed the character of a University. In it those great libraries were collected, the pride and boast of antiquity. Demetrius Phalareus was instructed to collect all the writings in the world. So powerfully were the exertions of himself and his successors enforced by the government that two immense libraries were procured. They contained 700,000 volumes. In this literary and scientific retreat, supported in ease and even in luxury—luxury, for allusions to the sumptuous dinners have descended to our times—the philosophers spent their time in mental culture by study, or mutual improvement by debates. The king himself conferred appointments to these positions; in later times, the Roman emperors succeeded to the patronage, the government thereby binding in golden chains intellect that might otherwise have proved troublesome. At first, in honour of the ancient religion, the presidency of the establishment was committed to an Egyptian priest; but in the course of time that policy was abandoned. It must not, however, be imagined that the duties of the inmates were limited to reading and rhetorical display; a far more Botanical gardens; menageries; dissecting-houses; observatories. practical character was imparted to them. A botanical garden, in connection with the Museum, offered an opportunity to those who were interested in the study of the nature of plants; a zoological menagerie afforded like facilities to those interested in animals. Even these costly establishments were made to minister to the luxury of the times: in the zoological garden pheasants were raised for the royal table. Besides these elegant and fashionable appointments, another, of a more forbidding and perhaps repulsive kind, was added; an establishment which, in the light of our times, is sufficient to confer immortal glory on those illustrious and high-minded kings, and to put to shame the ignorance and superstition of many modern nations: it was an anatomical school, suitably provided with means for the dissection of the human body, this anatomical school being the basis of a medical college for the education of physicians. For the astronomers Ptolemy Euergetes placed in the Square Porch an equinoctial and a solstitial armil, the graduated limbs of these instruments being divided into degrees and sixths. There were in the observatory stone quadrants, the precursors of our mural quadrants. On the floor a meridian line was drawn for the adjustment of the instruments. There were also astrolabes and dioptras. Thus, side by side, almost in the king's palace, were noble provisions for the cultivation of exact science and for the pursuit of light literature. Under the same roof were gathered together geometers, astronomers, chemists, mechanicians, engineers. There were also poets, who ministered to the literary wants of the dissipated city—authors who could write verse, not only in correct Life in the Museum. metre, but in all kinds of fantastic forms—trees, hearts, and eggs. Here met together the literary dandy and the grim theologian. At their repasts occasionally the king himself would preside, enlivening the moment with the condescensions of royal relaxation. Thus, of Philadelphus it is stated that he caused to be presented to the Stoic Sphærus a dish of fruit made of wax, so beautifully coloured as to be undistinguishable from the natural, and on the mortified philosopher detecting too late the fraud that had been practised upon him, inquired what he now thought of the maxim of his sect that "the sage is never deceived by appearances." Of the same sovereign it is related that he received the translators of the Septuagint Bible with the highest honours, entertaining them at his table. Under the atmosphere of the place their usual religious ceremonial was laid aside, save that the king courteously requested one of the aged priests to offer an extempore prayer. It is naively related that the Alexandrians present, ever quick to discern rhetorical merit, testified their estimation of the performance with loud applause. But not alone did literature and the exact sciences thus find protection. As if no subjects with which the human mind has occupied itself can be unworthy of investigation, in the Museum were cultivated the more doubtful arts, magic and astrology. Philadelphus, who, toward the close of his life, was haunted with an intolerable dread of death, devoted himself with intense assiduity to the discovery of the elixir of life and to alchemy. Such a comprehensive organization for the development of human knowledge never existed in the world before, and, considering the circumstances, never has since. To be connected with it was the passport to the highest Alexandrian society and to court favour.

The Septuagint translators.

To the Museum, and, it has been asserted, particularly to Ptolemy Philadelphus, the Christian world is thus under obligation for the ancient version of the Hebrew Scriptures—the Septuagint. Many idle stories have been related respecting the circumstances under which that version was made, as that the seventy-two translators by whom it was executed were confined each in a separate cell, and, when their work was finished, the seventy-two copies were found identically the same, word for word, from this it was supposed that the inspiration of this translation was established. If any proof of that kind were needed, it would be much better found in the fact that whenever occasion arises in the New Testament of quoting from the Old, it is usually done in the words of the Septuagint. The story of the cells underwent successive improvements among the early fathers, but is now rejected as a fiction; and, indeed, it seems probable that the translation was not made under the splendid circumstances commonly related, but merely by the Alexandrian Jews for their own convenience. As the Septuagint grew into credit among the Christians, it lost favour among the Jews, who made repeated attempts in after years to supplant it by new versions, such as those of Aquila, of Theodotion, of Symmachus, and others. From the first the Syrian Jews had looked on it with disapproval; they even held the time of its translation as a day of mourning, and with malicious grief pointed out its errors, as, for instance, they affirmed that it made Methusaleh live until after the Deluge. Ptolemy treated all those who were concerned in providing books for the library with consideration, remunerating his translators and transcribers in a princely manner.

Lasting influence of the Museum, theological and scientific.

But the modern world is not indebted to these Egyptian kings only in the particular here referred to. The Museum made an impression upon the intellectual career of Europe so powerful and enduring that we still enjoy its results. That impression was twofold, theological and physical. The dialectical spirit and literary culture diffused among the Alexandrians prepared that people, beyond all others, for the reception of Christianity. For thirty centuries the Egyptians had been familiar with the conception of a triune God. There was hardly a city of any note without its particular triad. Here it was Amun, Maut, and Khonso; there Osiris, Isis, and Horus. The apostolic missionaries, when they reached Alexandria, found a people ready to appreciate the profoundest mysteries. But with these advantages came great evils. The Trinitarian disputes, which subsequently deluged the world with blood, had their starting-point and focus in Alexandria. In that city Arius and Athanasius dwelt. There originated that desperate conflict which compelled Constantine the Great to summon the Council of Nicea, to settle, by a formulary or creed, the essentials of our faith.

But it was not alone as regards theology that Alexandria exerted a power on subsequent ages; her influence was as strongly marked in the impression it gave to science. Astronomical observatories, chemical laboratories, libraries, dissecting-houses, were not in vain. There went forth from them a spirit powerful enough to tincture all future times. Nothing like the Alexandrian Museum was ever called into existence in Greece or Rome, even in their palmiest days. It is the unique and noble memorial of the dynasty of the Ptolemies, who have thereby laid the whole human race under obligations, and vindicated their title to be regarded as a most illustrious line of kings. The Museum was, in truth, an attempt at the organization of human knowledge, both for its development and its diffusion. It was conceived and executed in a practical manner worthy of Alexander. And though, in the night through which Europe has been passing—a night full of dreams and delusions—men have not entertained a right estimate of the spirit in which that great institution was founded, and the work it accomplished, its glories being eclipsed by darker and more unworthy things, the time is approaching when its action on the course of human events will be better understood, and its influences on European civilization more clearly discerned.

The Museum was the issue of the Macedonian campaigns.

Thus, then, about the beginning of the third century before Christ, in consequence of the Macedonian campaign, which had brought the Greeks into contact with the ancient civilization of Asia, a great degree of intellectual activity was manifested in Egypt. On the site of the village of Rhacotis, once held as an Egyptian post to prevent the ingress of strangers, the Macedonians erected that city which was to be the entrepôt of the commerce of the East and West, and to transmit an illustrious name to the latest generations. Her long career of commercial prosperity, her commanding position as respects the material interests of the world, justified the statesmanship of her founder, and the intellectual glory which has gathered round her has given an enduring lustre to his name.

There can be no doubt that the philosophical activity here alluded to was the direct issue of the political and military event to which we have referred it. The tastes and genius of Alexander were manifested by his relations to Aristotle, whose studies in natural history he promoted by the collection of a menagerie; and in astronomy, by transmitting to him, through Callisthenes, the records of Babylonian observations extending over 1903 years. His biography, as we have seen, shows a personal interest in the cultivation of such studies. In this particular other great soldiers have resembled him; and perhaps it may be inferred that the practical habit of thought and accommodation of theory to the actual purposes of life pre-eminently required by their profession, leads them spontaneously to decline speculative uncertainties, and to be satisfied only with things that are real and exact.

Under the inspiration of the system of Alexander, and guided by the suggestions of certain great men who had caught the spirit of the times, the Egyptian kings thus created, under their own immediate auspices, the Museum. State policy, operating in the manner I have previously described, furnished them with an additional theological reason for founding this establishment. In the Macedonian campaign a vast amount of engineering and mathematical talent had been necessarily stimulated into existence, for great armies cannot be handled, great marches cannot be made, nor great battles fought without that result. When the period of energetic action was over, and to the military operations succeeded comparative repose and temporary moments of peace, the talent thus called forth found occupation in the way most congenial to it by cultivating mathematical and physical studies. In Alexandria, itself a monument of engineering and architectural skill, soon were to be found men whose names were destined for The great men it produced. futurity—Apollonius, Eratosthenes, Manetho. Of these, one may be selected for the remark that, while speculative philosophers were occupying themselves with discussions respecting the criterion of truth, and, upon the whole, coming to the conclusion that no such thing existed, and that, if the truth was actually in the possession of man, he had no means of knowing it, Euclid of Alexandria was writing an immortal work, destined to challenge contradiction from the whole human race, and to make good its title as the representative of absolute and undeniable truth—truth not to be gainsaid in any nation or at any time. We still use the geometry of Euclid in our schools.

The writings of Euclid.

It is said that Euclid opened a geometrical school in Alexandria about B.C. 300. He occupied himself not only with mathematical, but also with physical investigation. Besides many works of the former class supposed to have been written by him, as on Fallacies, Conic Sections, Divisions, Porisms, Data, there are imputed to him treatises on Harmonics, Optics, and Catoptrics, the two latter subjects being discussed, agreeably to the views of those times, on the hypothesis of rays issuing from the eye to the object, instead of passing, as we consider them to do, from the object to the eye. It is, however, on the excellencies of his Elements of Geometry that the durable reputation of Euclid depends; and though the hypercriticism of modern mathematicians has perhaps successfully maintained such objections against them as that they might have been more precise in their axioms, that they sometimes assume what might be proved, that they are occasionally redundant, and their arrangement sometimes imperfect, yet they still maintain their ground as a model of extreme accuracy, of perspicuity, and as a standard of exact demonstration. They were employed universally by the Greeks, and, in subsequent ages, were translated and preserved by the Arabs.

The writings and works of Archimedes.

Great as is the fame of Euclid, it is eclipsed by that of Archimedes the Syracusan, born B.C. 287, whose connection with Egyptian science is not alone testified by tradition, but also by such facts as his acknowledged friendship with Conon of Alexandria, and his invention of the screw still bearing his name, intended for raising the waters of the Nile. Among his mathematical works, the most interesting, perhaps, in his own estimation, as we may judge from the incident that he directed the diagram thereof to be engraved on his tombstone, was his demonstration that the solid content of a sphere is two-thirds that of its circumscribing cylinder. It was by this mark that Cicero, when Quæstor of Sicily, discovered the tomb of Archimedes grown over with weeds. This theorem was, however, only one of a large number of a like kind, which he treated of in his two books on the sphere and cylinder in an equally masterly manner, and with equal success. His position as a geometer is perhaps better understood from the assertion made respecting him by a modern mathematician, that he came as near to the discovery of the Differential Calculus as can be done without the aid of algebraic transformations. Among the special problems he treated of may be mentioned the quadrature of the circle, his determination of the ratio of the circumference to the diameter being between: 3·1428 and 3·1408, the true value, as is now known, being 3·1416 nearly. He also wrote on Conoids and Spheroids, and upon that spiral still passing under his name, the genesis of which had been suggested to him by Conon. In his work entitled "Psammites" he alludes to the astronomical system subsequently established by Copernicus, whose name has been given to it. He also mentions the attempts which had been made to measure the size of the earth; the chief object of the work being, however, to prove not only that the sands upon the sea-shore can be numbered, but even those required to fill the entire space within the sphere of the fixed stars; the result being, according to our system of arithmetic, a less number than is expressed by unity followed by 63 ciphers. Such a book is the sport of a geometrical giant wantonly amusing himself with his strength. Among his mathematical investigations must not be omitted the quadrature of the parabola. His fame depends, however, not so much on his mathematical triumphs as upon his brilliant discoveries in physics and his mechanical inventions. How he laid the foundation of Hydrostatics is familiar to everyone, through the story of Hiero's crown. A certain artisan having adulterated the gold given him by King Hiero to form a crown, Archimedes discovered while he was accidentally stepping into a bath, that the falsification might be detected, and thereby invented the method for the determination of specific gravity. From these investigations he was naturally led to the consideration of the equilibrium of floating bodies; but his grand achievement in the mechanical direction was his discovery of the true theory of the lever: his surprising merit in these respects is demonstrated by the fact that no advance was made in theoretical mechanics during the eighteen centuries intervening between him and Leonardo da Vinci. Of minor matters not fewer than forty mechanical inventions have been attributed to him. Among these are the endless screw, the screw pump, a hydraulic organ, and burning mirrors. His genius is well indicated by the saying popularly attributed to him, "Give me whereon to stand, and I will move the earth," and by the anecdotes told of his exertions against Marcellus during the siege of Syracuse; his invention of catapults and other engines for throwing projectiles, as darts and heavy stones, claws which, reaching over the walls, lifted up into the air ships and their crews, and then suddenly dropped them into the sea; burning mirrors, by which, at a great distance, the Roman fleet was set on fire. It is related that Marcellus, honouring his intellect, gave the strictest orders that no harm should be done to him at the taking of the town, and that he was killed, unfortunately, by an ignorant soldier—unfortunately, for Europe was not able to produce his equal for nearly two thousand years.

The writings and works of Eratosthenes.

Eratosthenes was contemporary with Archimedes. He was born at Cyrene, B.C. 276. The care of the library appears to have been committed to him by Euergetes; but his attention was more specially directed to mathematical, astronomical, geographical, and historical pursuits. The work entitled "Catasterisms," doubtfully imputed to him, is a catalogue of 475 of the principal stars; but it was probably intended for nothing more than a manual. He also is said to have written a poem upon terrestrial zones. Among his important geographical labours may be mentioned his determination of the interval between the tropics. He found it to be eleven eighty-thirds of the circumference. He also attempted the measurement of the size of the earth by ascertaining the distance between Alexandria and Syene, the difference of latitude between which he had found to be one-fiftieth of the earth's circumference. It was his object to free geography from the legends with which the superstition of ages had adorned and oppressed it. In effecting this he well deserves the tribute paid to him by Humboldt, the modern who of all others could best appreciate his labours. He considered the articulation and expansion of continents; the position of mountain chains; the action of clouds; the geological submersion of lands; the elevation of ancient sea-beds; the opening of the Dardanelles and of the Straits of Gibraltar; the relations of the Euxine Sea; the problem of the equal level of the circumfluous ocean; and the necessary existence of a mountain chain running through Asia in the diaphragm of Dicæarchus. What an advance is all this beyond the meditations of Thales! Herein we see the practical tendencies of the Macedonian wars. In his astronomical observations he had the advantage of using the armils and other instruments in the Observatory. He ascertained that the direction of terrestrial gravity is not constant, but that the verticals converge. He composed a complete systematic description of the earth in three books—physical, mathematical, historical—accompanied by a map of all the parts then known. Of his skill as a geometer, his solution of the problem of two mean proportionals, still extant, offers ample evidence; and it is only of late years that the fragments remaining of his Chronicles of the Theban Kings have been properly appreciated. He hoped to free history as well as geography from the myths that deform it, a task which the prejudices and interests of man will never permit to be accomplished. Some amusing anecdotes of his opinions in these respects have descended to us. He ventured to doubt the historical truth of the Homeric legends. "I will believe in it when I have been shown the currier who made the wind-bags which Ulysses on his homeward voyage received from Æolus." It is said that, having attained the age of eighty years, he became weary of life, and put an end to himself by voluntary starvation.

Chronology of Eratosthenes.

I shall here pause to make a few remarks suggested by the chronological and astronomical works of Eratosthenes. Our current chronology was the offspring of erroneous theological considerations, the nature of which required not only a short historical term for the various nations of antiquity, but even for the existence of man upon the globe. This necessity appears to have been chiefly experienced in the attempt to exalt certain facts in the history of the Hebrews from their subordinate position in human affairs, and, indeed, to give the whole of that history an exaggerated value. This was done in a double way: by elevating Hebrew history from its true grade, and depreciating or falsifying that of other nations. Among those who have been guilty of this literary offence, the name of the celebrated Eusebius, the Bishop of Cæsarea in the time of Constantine, should be designated, since in his chronography and synchronal tables he purposely "perverted chronology for the sake of making synchronisms" (Bunsen). It is true, as Niebuhr asserts, "He is a very dishonest writer." To a great extent, the superseding of the Egyptian annals was brought about by his influence. It was forgotten, however, that of all things chronology is the least suited to be an object of inspiration; and that, though men may be wholly indifferent to truth for its own sake, and consider it not improper to wrest it unscrupulously to what they may suppose to be a just purpose, yet that it will vindicate itself at last. It is impossible to succeed completely in perverting the history of a nation which has left numerous enduring records. Egypt offers us testimonials reaching over five thousand years. As Bunsen remarks, from the known portion of the curve of history we may determine the whole. The Egyptians, old as they are, belong to the middle ages of mankind, for there is a period antecedent to monumental history, or indeed, to history of any kind, during which language and mythology are formed, for these must exist prior to all political institutions, all art, all science. Even at the first moment that we gain a glimpse of the state of Egypt she had attained a high intellectual condition, as is proved by the fact that her system of hieroglyphics was perfected before the fourth dynasty. It continued unchanged until the time of Psammetichus. A stationary condition of language and writing for thousands of years necessarily implies a long and very remote period of active improvement and advance. It was doubtless such a general consideration, rather than a positive knowledge of the fact, which led the Greeks to assert that the introduction of geometry into Egypt must be attributed to kings before the times of Menes. Not alone do her artificial monuments attest for that country an extreme antiquity; she is herself her own witness; for, though the Nile raises its bed only four feet in a thousand years, all the alluvial portion of Egypt has been deposited from the waters of that river. A natural register thus re-enforces the written records, and both together compose a body of evidence not to be gainsaid. Thus the depth of muddy silt accumulated round the pedestals of monuments is an irreproachable index of their age. In the eminent position he occupied, Eusebius might succeed in perverting the received book-chronology; but he had no power to make the endless trade-wind that sweeps over the tropical Pacific blow a day more or a day less; none to change the weight of water precipitated from it by the African mountains; none to arrest the annual mass of mud brought down by the river. It is by collating such different orders of evidence together—the natural and the monumental, the latter gaining strength every year from the cultivation of hieroglyphic studies—that we begin to discern the true Egyptian chronology, and to put confidence in the fragments that remain of Eratosthenes and Manetho.